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PAPER-4AZwH«$‘m§H$ / Roll No.
CÎma-erQ> H«$‘m§H$ / OMR Answer Sheet No.
KmofUm : / Declaration :‘¢Zo n¥îR> g§»¶m 1 na {X¶o J¶o {ZX}em| H$mo n‹T>H$a g‘P {b¶m h¡&I have read and understood the instructions given on page No. 1
narjmWu H$m hñVmja /Signature of Candidate(AmdoXZ nÌ Ho$ AwZgma /as signed in application)
narjm Ho$ÝÐmܶj H$s ‘mohaSeal of Superintendent of Examination Centre
narjmWu H$m Zm‘/Name of Candidate :
àíZnwpñVH$m H«$‘m§H$Question Booklet Sr. No. DC
Q. Booklet Code
narjm{W©¶m| Ho$ {bE {ZX}e /INSTRUCTIONS TO CANDIDATE
narjmWu H$mo {X¶o n¡amJ«m’$ H$s ZH$b ñd¶§ H$s hñV{b{n ‘| ZrMo {X¶o J¶o [a³V ñWmZ na ZH$b (H$m°nr) H$aZr h¡&""Amn ghr ì¶dgm¶ ‘| h¢, ¶h Amn V^r OmZ|Jo O~ : Amn H$m‘ na OmZo Ho$ {bE qM{VV h¢, Amn {Z˶ AnZm H$m‘ g~go AÀN>m H$aZm MmhVo h¢, Am¡a Amn AnZo H$m¶© Ho$ ‘hËd H$mo g‘PVo h¢&'' AWdm / OR To be copied by the candidate in your own handwriting in the space given below for this purpose is compulsory.‘‘You will know you are in the right profession when : you wake anxious to go to work, you want to do your best daily, and you know your work is important.”
Aä¶{W©¶m| hoVw Amdí¶H$ {ZX}e : Instructions for the Candidate :1. Amo.E‘.Ama. CÎma n{ÌH$m ‘| Jmobm| VWm g^r à{dpîQ>¶m| H$mo ^aZo Ho$ {bE Ho$db
Zrbo ¶m H$mbo ~mb ßdmB§Q> noZ H$m hr Cn¶moJ H$a|&1. UseBLUEorBLACKBALLPOINTPENonlyforallentriesandforfilling
the bubbles in the OMR Answer Sheet.
2. SECURITY SEAL ImobZo Ho$ nhbo Aä¶Wu AnZm Zm‘, AZwH«$‘m§H$ (A§H$m| ‘|) Amo.E‘.Ama. CÎma-erQ> H$m H«$‘m§H$ Bg àíZ-nwpñVH$m Ho$ D$na {X¶o J¶o ñWmZ na {bI|& ¶{X do Bg {ZX}e H$m nmbZ Zht H$a|Jo Vmo CZH$s CÎma-erQ> H$m ‘yë¶m§H$Z Zhr hmo gHo$Jm VWm Eogo Aä¶Wu A¶mo½¶ Kmo{fV hmo Om¶|Jo&
2. Before opening the SECURITY SEAL of the question booklet, write yourName,RollNumber(Infigures),OMRAnswer-sheetNumberinthespaceprovidedatthetopoftheQuestionBooklet.Non-complianceof these instructions would mean that the Answer Sheet can not be evaluatedleadingthedisqualificationofthecandidate.
3. à˶oH$ àíZ Mma A§H$m| H$m h¡& {Og àíZ H$m CÎma Zht {X¶m J¶m h¡, Cg na H$moB© A§H$ Zht {X¶m Om¶oJm& JbV CÎma na A§H$ Zht H$mQ>m OmEJm&
3. Each question carries FOUR marks. No marks will be awarded for unattempted questions. There is no negative marking on wrong answer.
4. g^r ~hþ{dH$ënr¶ àíZm| ‘| EH$ hr {dH$ën ghr h¡, {Ogna A§H$ Xo¶ hmoJm& 4. Each multiple choice questions has only one correct answer and marks shall be awarded for correct answer.
5. JUH$, bm°J Q>o{~b, ‘mo~mBb ’$moZ, Bbo³Q´>m°{ZH$ CnH$aU VWm ñbmBS> ê$b Am{X H$m à¶moJ d{O©V h¡&
5. Use of calculator, log table, mobile phones, any electronic gadget and slide rule etc. is strictly prohibited.
6. Aä¶Wu H$mo narjm H$j N>moS>Zo H$s AZw‘{V narjm Ad{Y H$s g‘mpßV na hr Xr Om¶oJr&
6. Candidate will be allowed to leave the examination hall at the end of examination time period only.
7. ¶{X {H$gr Aä¶Wu Ho$ nmg nwñVH|$ ¶m Aݶ {b{IV ¶m N>nr gm‘J«r, {Oggo do ghm¶Vm bo gH$Vo/gH$Vr h¢, nm¶r Om¶oJr, Vmo Cgo A¶mo½¶ Kmo{fV H$a {X¶m Om gH$Vm h¡& Bgr àH$ma, ¶{X H$moB© Aä¶Wu {H$gr ^r àH$ma H$s ghm¶Vm {H$gr ^r ómoV go XoVm ¶m boVm (¶m XoZo H$m ¶m boZo H$m à¶mg H$aVm) hþAm nm¶m Om¶oJm, Vmo Cgo ^r A¶mo½¶ Kmo{fV {H$¶m Om gH$Vm h¡&
7. If a candidate is found in possession of books or any other printed or written material from which he/she might derive assistance, he/she isliabletobetreatedatdisqualified.Similarly,ifacandidateisfoundgiving or obtaining (or attempting to give or obtain) assistance from any source,he/sheisliabletobedisqualified.
8. {H$gr ^r ^«‘ H$s Xem ‘| àíZ-nwpñVH$m Ho$ A§J«oOr A§e H$mo hr ghr d A§{V‘ ‘mZm Om¶oJm&
8. English version of questions paper is to be considered as authentic and finaltoresolveanyambiguity.
9. a’$ H$m¶© Ho$ {bE EH$ Imbr sheet g§½b½Z h¡& 9. One blank sheet for rough work is also enclosed.10. OMR sheet Bg Paper Ho$ ^rVa h¡ VWm Bgo ~mha {ZH$mbm Om gH$Vm h¡ naÝVw
Paper H$s grb Ho$db nona ewé hmoZo Ho$ g‘¶ na hr Imobm Om¶oJm&10. OMR sheet is placed within this paper and can be taken out from this
paper but seal of paper must be opened only at the start of paper.
PAPER-4AZwH«$‘m§H$ / Roll No.
DCQ. Booklet Code
H$j {ZarjH$ Ho$ hñVmja /Signature of the Invigilator
àíZnwpñVH$m H$moS>
àíZnwpñVH$m H$moS>
àíZnwpñVH$m H«$‘m§H$/ Question Booklet Sr. No.
H$j {ZarjH$ Ho$ hñVmja /Signature of the Invigilator
* Bg n¥îR> H$m D$nar AmYm ^mJ H$mQ>Zo Ho$ ~mX drjH$ Bgo N>mÌ H$s OMR sheet Ho$ gmW gwa{jV aIo&* After cutting half upper part of this page, invigilator preserve it along with student’s OMR sheet.
narjmWu H$m Zm‘/Name of Candidate :
Aptitude Test for ArchitecturePART-A : Mathematics & Aesthetic SensitivityPART-B : Drawing Aptitude
Aptitude Test for ArchitecturePART-A : Mathematics & Aesthetic SensitivityPART-B : Drawing Aptitude
nwpñVH$m ‘| ‘wIn¥îR> g{hV n¥îR>m| H$s g§»¶mNo. of Pages in Booklet including title
32 g‘¶ 2.30 K§Q>oTime 2.30 Hours
A§H$ / Marks 500
nwpñVH$m ‘| àíZm| H$s g§»¶mNo. of Questions in Booklet
100 Questions &
Drawing Sheet
4 - DC ] [ 2 ] [ Contd...
PART-A / ^mJ-AMATHEMATICS & AESTHETICS SENSITIVITY / J{UV Am¡a EñWo{Q>H$ g|{gQ>r{dQ>r
001. If 1107
A=-> H &
1001
I= > H , then
find K so that A2 = 8A + KI.
(A) – 3
(B) 9
(C) – 5
(D) – 7
001. ¶{X 1107
A=-> H &
1001
I= > H , Vmo K H$m
‘mZ ¶{X A2 = 8A + KI.
(A) – 3
(B) 9
(C) – 5
(D) – 7
PAPER-4Aptitude Test for ArchitectureMathematics & Aesthetic Sensitivity – Part A : Q. 1 to 100Drawing Aptitude – Part B : Q. 1 & 2
4 - DC ] [ 3 ] [ PTO
002. If 213
104-
-R
T
SSSS
V
X
WWWW A =
119
8222
10515
- -
-
-
-
R
T
SSSS
V
X
WWWW what
will be A?
(A) A = 37
24
72-
-> H
(B) A = 13
24
50
- -> H
(C) None of these
(D) A = 72
46
02-
-
-> H
003. What will be the maximum value of the function f (x) = – (x – 1)2 + 2 on R?
(A) 3 (B) 1 (C) 2 (D) 4
004. Find the maximum & minimum value of the function f (x) = |sin4x + 3| on R?
(A) Max – 4 Min – 2
(B) Max – 5 Min – 2
(C) Max – 3 Min – 1
(D) None of these
005. What will be the point of local maximum and local maximum value of the function ( ) ,f x x x x1 0>= -
(A) Point of local max x 21- = Local
max value 32 2-
(B) Point of local max x 32- = Local
max value 3 32-
(C) Point of local max x 23- = Local
max value 23 2-
(D) Point of local max x 41- = Local
max value 34 3-
002. ¶{X 213
104-
-R
T
SSSS
V
X
WWWW A =
119
8222
10515
- -
-
-
-
R
T
SSSS
V
X
WWWW Vmo
A H$m ‘mZ-
(A) A = 37
24
72-
-> H
(B) A = 13
24
50
- -> H
(C) BZ‘| go H$moB© Zht
(D) A = 72
46
02-
-
-> H
003. ’$bZ f (x) = – (x – 1)2 + 2 on R H$m A{YH$V‘ ‘mZ ³¶m hmoJm -
(A) 3 (B) 1 (C) 2 (D) 4
004. ’$bZ f (x) = |sin4x + 3| on R H$m A{YH$V‘ ‘mZ ³¶m hmoJm?
(A) A{YH$V‘ – 4 ݶyZV‘ – 2
(B) A{YH$V‘ – 5 ݶyZV‘ – 2
(C) A{YH$V‘ – 3 ݶyZV‘ – 1
(D) BZ‘| go H$moB© Zht
005. ’$bZ ( ) ,f x x x x1 0>= - Ho$ {bE A{YH$V‘
ñWmZr` d A{YH$V‘ ñWmZr` ‘mZ hmoJm-
(A) Point of local max x 21- = Local
max value 32 2-
(B) Point of local max x 32- = Local
max value 3 32-
(C) Point of local max x 23- = Local
max value 23 2-
(D) Point of local max x 41- = Local
max value 34 3-
4 - DC ] [ 4 ] [ Contd...
006. If f (2) = 4 and f´(2) =1, then find
limx 2"
( ) ( )x
xf f x2
2 2-
-
(A) 1 (B) 0
(C) 2 (D) None of these
007. If ( ) 2 7f x x x2= + + , what will be f (3)
(A) 3 (B) 5
(C) 4 (D) 8
008. Let f (x) = | x | and g(x) = | x3|, then–
(A) f (x) and g (x) both are continous at x = 0
(B) f(x) and g(x) both are differentiable at x = 0
(C) f(x) is differentiable but g(x) is not differentiable at x = 0
(D) f(x) and g (x) both are not differentiable at x = 0
009. Let f (x) = (x + | x |) | x |. Then for all x
(A) f is continuous
(B) f is differentiable for some x
(C) f ′ is continuous
(D) f & f ′ both are continuous
006. ¶{X f (2) = 4 Am¡a f´(2) =1, Vmo
limx 2"
( ) ( )x
xf f x2
2 2-
- H$m ‘mZ hmoJm -
(A) 1 (B) 0
(C) 2 (D) BZ‘| go H$moB© Zht
007. ¶{X ( ) 2 7f x x x2= + + , hmo Vmo f (3) H$m ‘mZ
³¶m hmoJm -
(A) 3 (B) 5
(C) 4 (D) 8
008. ‘mZm f (x) = | x | d g(x) = | x3|, Vmo -
(A) f (x) and g (x) both are continous at x = 0
(B) f(x) and g(x) both are differentiable at x = 0
(C) f(x) is differentiable but g(x) is not differentiable at x = 0
(D) f(x) and g (x) both are not differentiable at x = 0
009. ‘mZm f (x) = (x + | x |) | x |. Vmo Hw$b x Ho$ {bE-
(A) f is continuous
(B) f is differentiable for some x
(C) f ′ is continuous
(D) f & f ′ both are continuous
4 - DC ] [ 5 ] [ PTO
010. ABCD is a parallelogram. If the coordinates of A, B, C are (2, 3), (2, 4) and (0, – 2) respectively, what will the coordinate of D.
(A) x = 2, y = – 1
(B) x = 3, y = – 2
(C) x = 1, y = – 3
(D) None of these
011. If ` 85 amounts to ` 95 in 3 years, what ` 102 will amount in 5 years at the same rate %?
(A) 117 (B) 122
(C) 132 (D) 142
012. If x1 64 89+ = , than x = ?
(A) 15 (B) 16
(C) 17 (D) 18
013. If ,x x1 5+ = then value of ?,x
x122+ =
(A) 21 (B) 23
(C) 25 (D) 27
014. The cube root of 0.00000729 is -
(A) 0.0027
(B) 0.027
(C) 0.0009
(D) 0.009
010. ABCD EH$ MVw^w©©O h¡ `{X A, B, C Ho$ {ZX}em§H$ H«$‘e: (2, 3), (2, 4) d (0, -2) hmo Vmo D erf© Ho$ {ZX}em§H$ Š`m hm|Jo?
(A) x = 2, y = -1
(B) x = 3, y = -2
(C) x = 1, y = -3
(D) BZ‘| go H$moB© Zht
011. `{X ` 85 H$m {‘lYZ 3 dfm}§ ‘| ` 95 hmo Vmo ` 102 H$m 5 dfm}§ ‘| Cgr ã`mO Xa go {‘lYZ
Š`m hmoJm?
(A) 117 (B) 122
(C) 132 (D) 142
012. `{X, x1 64 89+ = , hmo Vmo x H$m ‘mZ hmoJm &
(A) 15 (B) 16
(C) 17 (D) 18
013. `{X, ,x x1 5+ = Vmo ?,x
x122+ = H$m ‘mZ
~VmAmo-
(A) 21 (B) 23
(C) 25 (D) 27
014. 0.00000729 H$m KZ‘yb Š`m hmoJm-
(A) 0.0027
(B) 0.027
(C) 0.0009
(D) 0.009
4 - DC ] [ 6 ] [ Contd...
015. Find the value of x if
x1 25633 1 16+ = +d n 9 C
(A) 1 (B) 2
(C) 4 (D) 3
016. Which is the Term of 1280 in Series 5, 10, 20, 40, ...............?
(A) 7th
(B) 10th
(C) 9th
(D) None of these
017. If (k – 2, (2k +1), (6 k + 3) are in GP, then k = ?
(A) 2 (B) 7
(C) 3 (D) 6
018. The 3rd term of a G.P. is 4. What will be the total sum of the first five terms of this GP?
(A) 1024
(B) 1248
(C) 1368
(D) 1092
019. Which term of AP 3, 18, 13, ........ is 78? (A) A23 (B) A19
(C) A16
(D) A22
015. `{X x1 25633 1 16+ = +d n 9 C hmo Vmo x H$m
‘mZ Š`m hmoJm-
(A) 1 (B) 2
(C) 4 (D) 3
016. loUr 5, 10, 20, 40, ............... H$m H$m¡Z-gm nX 1280 h¡?
(A) 7th
(B) 10th
(C) 9th
(D) BZ‘| go H$moB© Zht
017. `{X (k – 2, (2k +1), (6 k + 3) JwUmoËVa loUr ‘| hmo Vmo k H$m ‘mZ Š`m hmoJm?
(A) 2 (B) 7
(C) 3 (D) 6
018. JwUmoËVa loUr H$m Vrgam nX 4 h¡ Vmo JwUmoËVa loUr Ho$ àW‘ nm±M nXm| H$m `moJ Š`m hmoJm?
(A) 1024
(B) 1248
(C) 1368
(D) 1092
019. g‘mÝVa loUr 3, 18, 13, ........ H$m H$m¡Z-gm nX 78 h¡?
(A) A23 (B) A19
(C) A16
(D) A22
4 - DC ] [ 7 ] [ PTO
020. Which term of the AP 3, 15, 27, 39.......... will be 132 more than its 54th term?
(A) 57 (B) 92
(C) 63 (D) 65
021. Evaluating cos(tan– 1 x) we get :–
(A) x11
2+
-
(B) x1 2+
(C) x1
12
+
(D) 1
022. If x, y, z ∈ [– 1, 1] such that
sin– 1 x + sin– 1 y z = ,23p find the value of
x y zx y z
92006 2007 20082006 2007 2008+ + -+ +
(A) 0 (B) 1
(C) – 1 (D) 2
023. Evaluate tan cos21
351-( 2 we get –
(A) 23 5-
(B) 25 3+
(C) 2
(D) 1
020. g‘mÝVa loUr 3, 15, 27, 39.......... H$m H$m¡Z-gm nX 54d| nX go 132 A{YH$ hmoJm?
(A) 57 (B) 92
(C) 63 (D) 65
021. cos(tan– 1 x) H$mo hb H$aZo na Š`m àmá hmoJm-
(A) x11
2+
-
(B) x1 2+
(C) x1
12
+
(D) 1
022. `{X x, y, z ∈ [– 1, 1] Bgr àH$ma
sin– 1 x + sin– 1 y z = ,23p hmo, Vmo
x y zx y z
92006 2007 20082006 2007 2008+ + -+ +
H$m ‘mZ Š`m hmoJm?
(A) 0 (B) 1
(C) – 1 (D) 2
023. tan cos21
351-( 2 H$mo hb H$aZo na Š`m àmá
hmoJm-
(A) 23 5-
(B) 25 3+
(C) 2
(D) 1
4 - DC ] [ 8 ] [ Contd...
024. If a b
ab52+
> H = 6528
> H, find the value of
a and b.
(A) 4, 5
(B) 2, 4
(C) 4, 2
(D) 0, 1
025. Simplify -
coscossin
sincos
sinsincos
cossin
qqq
qqq
qq-
+-
> >H H
(A) 1101
> H (B) 1001
> H
(C) 11
11
> H (D) 1415
> H
026. Find a matrix A, if -
2134
33
68
A=-
=-
-> >H H
(A) 12
94-
-> H
(B) 10
42-
> H
(C) 1414-
> H
(D) 21
94
- -
-> H
024. `{X a b
ab52+
> H = 6528
> H, hmo Vmo a Am¡a b H$m
‘mZ Š`m hmoJm-
(A) 4, 5
(B) 2, 4
(C) 4, 2
(D) 0, 1
025. gab H$s{OE-
coscossin
sincos
sinsincos
cossin
qqq
qqq
qq-
+-
> >H H
(A) 1101
> H (B) 1001
> H
(C) 11
11
> H (D) 1415
> H
026. `{X
2134
33
68
A=-
=-
-> >H H hmo Vmo ‘¡{Q´Šg A
H$m ‘mZ Š`m hmoJm-
(A) 12
94-
-> H
(B) 10
42-
> H
(C) 1414-
> H
(D) 21
94
- -
-> H
4 - DC ] [ 9 ] [ PTO
027. If f (x) =x aabab
abx bbc
acbcx c
2
2
2
+
+
+
, find f (x)
(A) 3 2x x a b c2 2 2 2+ + +_ i
(B) 2 4x x a b2 2 2+ +_ i
(C) 4 2x x bx2+ +
(D) 4 3x x a b c2+ + +_ i
028. If x
x x2
332
3- -
= , find the value of x
(A) 21 , – 3
(B) 3, 3
(C) 4, 2
(D) – 3,
029. If from a pack of 52 playing cards, one card is drawn at random. What is the probability that it is either a king or queen?
(A) 131
(B) 132
(C) 263
(D) 521
027. `{X f (x) =x aabab
abx bbc
acbcx c
2
2
2
+
+
+
, hmo Vmo
f (x) H$m ‘mZ Š`m hmoJm-
(A) 3 2x x a b c2 2 2 2+ + +_ i
(B) 2 4x x a b2 2 2+ +_ i
(C) 4 2x x bx2+ +
(D) 4 3x x a b c2+ + +_ i
028. `{X x
x x2
332
3- -
= , hmo Vmo x H$m ‘mZ Š`m
hmoJm-
(A) 21 , – 3
(B) 3, 3
(C) 4, 2
(D) – 3,
029. `{X 52 Vmg Ho$ nËVm| ‘| go EH$ nËVm {~Zm H«$‘ Ho$ {ZH$mbm OmVm h¡ Vmo amOm `m amZr H$s {H$VZr àm{`H$Vm hmoJr?
(A) 131
(B) 132
(C) 263
(D) 521
4 - DC ] [ 10 ] [ Contd...
030. What is the Value of tan
tan
1 22 21
1 22 21
2
2
+
-
(A) 2
1
(B) 12
(C) 32
(D) 2
031. What is the value of 3 sin 20º – 4 sin3 20.
(A) 1 (B) 21
(C) 32 (D) 0
032. If 1–tan a2 2q = then sec tan cosec3q q q+ = ?
(A) (2– 3)3/2
(B) (2– a2)1/2
(C) (2– a2)2/3
(D) 1
033. The lines 2x – 3y & 3x – 4y = 7 are diameters of a circle of are 154 square units. An equator of this circle is (p = 22/7)
(A) 2 – 2 62x y x y2 2+ + =
(B) 2 – 2 47x y x y2 2+ + =
(C) – 2 2 47x y x y2 2+ + =
(D) – 2 2 62x y x y2 2+ + =
030. tan
tan
1 22 21
1 22 21
2
2
+
- H$m ‘mZ Š`m hmoJm-
(A) 2
1
(B) 12
(C) 32
(D) 2
031. 3 sin 20º – 4 sin3 20 H$m ‘mZ Š`m hmoJm?
(A) 1 (B) 21
(C) 32 (D) 0
032. `{X 1–tan a2 2q = Vmo sec tan cosec3q q q+ = H$m ‘mZ Š`m hmoJm?
(A) (2– 3)3/2
(B) (2– a2)1/2
(C) (2– a2)2/3
(D) 1
033. `{X aoIm 2x – 3y Am¡a 3x – 4y = 7 EH$ d¥ËV
H$m ì`mg h¡ Am¡a joÌ’$b 154 ‘r2 hmo Vmo d¥ËV
H$m g‘r. Š`m hmoJm (p = 22/7)
(A) 2 – 2 62x y x y2 2+ + =
(B) 2 – 2 47x y x y2 2+ + =
(C) – 2 2 47x y x y2 2+ + =
(D) – 2 2 62x y x y2 2+ + =
4 - DC ] [ 11 ] [ PTO
034. What will be the value of dxdy
if x – y = p?
(A) 1 (B) 3 (C) 1/4 (D) 1/2
035. Find dxdy
, if x = a(q + sin q),
y = a(1– cosq).
(A) sin2q
(B) cos 2q
(C) tan 2q
(D) tan2q
036. If xx1 722+ = , then x
x133+ will be?
(A) 38 (B) 29 (C) 18 (D) 28
037. If – ,ax bx c a x p2 2+ + = _ i then, what
is the relation between a, b, c? (A) 4b ac2
=
(B) 2b a c= +
(C) b ac2=
(D) 1abc =
038. x yx
x yy
y xxy2
2 2- + + +-
will be =?
(A) x y+
(B) 1
(C) – 1
(D) x yx y2 2
2 3
+
+
034. `{X x – y = p hmo Vmo dxdy
H$m ‘mZ Š`m hmoJm?
(A) 1 (B) 3 (C) 1/4 (D) 1/2
035. `{X x = a (q + sin q), y = a(1– cosq) hmo Vmo
dxdy
Š`m hmoJm?
(A) sin2q
(B) cos 2q
(C) tan 2q
(D) tan2q
036. `{X xx1 722+ = , Vmo x
x133+ H$m ‘mZ Š`m
hmoJm- (A) 38 (B) 29 (C) 18 (D) 28
037. `{X – ,ax bx c a x p2 2+ + = _ i hmo Vmo a, b,
c ‘| Š`m g§~§Y hmoJm- (A) 4b ac2
=
(B) 2b a c= +
(C) b ac2=
(D) 1abc =
038. x yx
x yy
y xxy2
2 2- + + +-
=?
(A) x + y
(B) 1
(C) – 1
(D) x yx y2 2
2 3
+
+
4 - DC ] [ 12 ] [ Contd...
039. 2 sin q = x x1+ , then
(A) x = ± 1
(B) – 1 < x < 1
(C) x = 1
(D) None of these
040. If x = tan 15º then what will be the value
of xx122+ .
(A) 16 (B) 12 (C) 10 (D) 14
041. If coscos
sinsin
2
4
2
4
βα
βα
+ = 1, then
coscos
sinsin
2
4
2
4
α
β
α
β+ will be -
(A) 4 (B) 0
(C) 81 (D) 1
042. If sin cos sin cosx y3 3q q q q+ = & x sin
q = y cos q, then x2 + y2 = ?
(A) 0 (B) 2
(C) 4 (D) 1
043. ?sin 22 21 =
(A) 22 2-
(B) 23 2-
(C) 2
2 2+
(D) 2
2 2-
039. 2 sin q = x x1+ , V~-
(A) x = ±1
(B) – 1 < x < 1
(C) x = 1
(D) BZ‘| go H$moB© Zht
040. `{X x = tan 15º Vmo xx122+ H$m ‘mZ Š`m
hmoJm-
(A) 16 (B) 12
(C) 10 (D) 14
041. `{X coscos
sinsin
2
4
2
4
βα
βα
+ = 1 Vmo coscos
sinsin
2
4
2
4
α
β
α
β+
H$m ‘mZ Š`m hmoJm-
(A) 4 (B) 0
(C) 81 (D) 1
042. `{X sin cos sin cosx y3 3q q q q+ = Am¡a x sin q = y cos q V~ x2 + y2 H$m ‘mZ Š`m hmoJm-
(A) 0 (B) 2 (C) 4 (D) 1
043. ?sin 22 21 = H$m ‘mZ hmoJm-
(A) 22 2-
(B) 23 2-
(C) 2
2 2+
(D) 2
2 2-
4 - DC ] [ 13 ] [ PTO
044. ax36 2
4
-f p, its factors will be
(A) x ax
ax6 6
2
2
2
- +d fn p
(B) 6 x ax
ax6
2 2
+ -d dn n
(C) 6 x ax
ax6
2 2
- +d dn n
(D) 6 x ax
ax6
2 2
- -d dn n
045. If a b c ab bc ca2 2 2+ + = + + , then
a b c3 3 3+ + will be equal to?
(A) 3 abc2
_ i
(B) 3a b c2 2 2
(C) 3abc
(D) None of these
046. In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?
(A) 43 (B) 110
(C) 51 (D) 7
3
047. What will be the value of x dx2
1
2
# after evaluating it?
(A) 98
(B) 52
(C) 76
(D) 57
044. ax36 2
4
-f p, H$m JwUZIÊS> hmoJm-
(A) x ax
ax6 6
2
2
2
- +d fn p
(B) 6 x ax
ax6
2 2
+ -d dn n
(C) 6 x ax
ax6
2 2
- +d dn n
(D) 6 x ax
ax6
2 2
- -d dn n
045. ¶{X a b c ab bc ca2 2 2+ + = + + , hmo Vmo
a b c3 3 3+ + {H$gHo$ ~am~a hmoJm?
(A) 3 abc2
_ i
(B) 3a b c2 2 2
(C) 3abc
(D) BZ‘| go H$moB© Zht
046. EH$ ñHy$b ‘| 1000 N>mÌm| ‘| go 430 b‹S>{H$`m±
h¢& 430 ‘| go 10% b‹S>{H$`m± H$jm ~mah ‘|
n‹T>Vr h¢ g§^m{dV b‹S>{H$`m| H$s àm{`H$Vm Š`m
hmoJr?
(A) 43 (B) 110
(C) 51 (D) 7
3
047. gab H$aZo na x dx2
1
2
# H$m ‘mZ Š`m hmoJm-
(A) 98
(B) 52
(C) 76
(D) 57
4 - DC ] [ 14 ] [ Contd...
048. What will be sin x dx1 20
4
+
p
w ?
(A) – 1 (B) 1 (C) 0 (D) None of these
049. What will be the value of x ex
0
1
w dx?
(A) 1 (B) 21
(C) 0 (D) None of these
050. If [1 × 1] x
1215
353
212
12 0=
R
T
SSSS
R
T
SSSS
V
X
WWWW
V
X
WWWW
, then what
will be x?
(A) – 1 or – 7 (B) – 2 or – 14
(C) – 3 or – 6 (D) – 4 or – 10
051. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
048. sin x dx1 20
4
+
p
w ? H$m ‘mZ Š`m hmoJm-
(A) – 1 (B) 1 (C) 0 (D) BZ‘| go H$moB© Zht
049. x ex
0
1
w dx H$m ‘mZ ³¶m hmoJm -
(A) 1 (B) 21
(C) 0 (D) BZ‘| go H$moB© Zht
050. ¶{X [1 × 1] x
1215
353
212
12 0=
R
T
SSSS
R
T
SSSS
V
X
WWWW
V
X
WWWW
, hmo Vmo x
H$m ‘mZ hmoJm?
(A) – 1 VWm – 7 (B) – 2 VWm – 14
(C) – 3 VWm – 6 (D) – 4 VWm – 10
051. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
4 - DC ] [ 15 ] [ PTO
052. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
053. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
052. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
053. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
4 - DC ] [ 16 ] [ Contd...
054. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
055. Select the correct figure from the options to continue the series to replace the question mark.
(A)
(B)
(C)
(D)
054. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
055. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(C)
(D)
4 - DC ] [ 17 ] [ PTO
056. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
057. Select the correct figure from the options to continue the series to replace the question mark.
(A)
(B)
(C)
(D)
056. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
057. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A)
(B)
(C)
(D)
4 - DC ] [ 18 ] [ Contd...
058. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
059. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
058. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
059. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
4 - DC ] [ 19 ] [ PTO
060. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
061. Write the missing numeral.
(A) 14
(B) 21
(C) 28
(D) 18
060. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
061. bwßV g§»`m kmV H$a|&
(A) 14
(B) 21
(C) 28
(D) 18
4 - DC ] [ 20 ] [ Contd...
062. Write the missing numeral.
(A) 3 (B) 2
(C) 1 (D) 8
063. How many faces/surfaces does this object have?
(A) 12
(B) 10
(C) 13
(D) 15
064. How many faces/surfaces does this object have?
(A) 14
(B) 15
(C) 12
(D) 13
062. bwßV g§»`m kmV H$a|&
(A) 3 (B) 2
(C) 1 (D) 8
063. ZrMo Xr JB© dñVw Ho$ Vbm| H$s Hw$b g§»`m kmV H$a|&
(A) 12
(B) 10
(C) 13
(D) 15
064. ZrMo Xr JB© dñVw Ho$ Vbm| H$s Hw$b g§»`m kmV H$a|&
(A) 14
(B) 15
(C) 12
(D) 13
4 - DC ] [ 21 ] [ PTO
065. The below diagram is the top view of an object. Identify the object with the given top view that cannot have the elevation from the side of the arrow.
(A)
(B)
(C)
(D)
065. àíZ {MÌ EH$ dñVw Ho$ D$na H$m Ñî` Xem©Vm h¡& {X`o JE {dH$ënm| ‘| go CgH$mo A§{H$V H$s{OE Omo Bg dñVw H$m {MpÝhV Ñí` Zht h¢&
(A)
(B)
(C)
(D)
4 - DC ] [ 22 ] [ Contd...
066. The below diagram is the top view of an object. Identify the front elevation of this object.
(A)
(B)
(C)
(D)
067. How many triangles are there in this figure?
(A) 27 (B) 25 (C) 23 (D) 21
066. àíZ {MÌ EH$ dñVw Ho$ D$na H$m Ñî` Xem©Vm h¡& {X`o JE {dH$ënm| go gm‘Zo dmbo ghr Ñí` H$mo nhMmZ| &
(A)
(B)
(C)
(D)
067. ZrMo {X`o J`o {MÌ ‘| {H$VZo {ÌH$moU h¢ ?
(A) 27 (B) 25 (C) 23 (D) 21
4 - DC ] [ 23 ] [ PTO
068. How many triangles are there in this figure?
(A) 23
(B) 27
(C) 29
(D) 31
069. How many squares are there in the figure below?
(A) 20
(B) 13
(C) 24
(D) 17
070. How many squares are there in the figure below?
(A) 18 (B) 19
(C) 25 (D) 27
068. ZrMo {X`o J`o {MÌ ‘| {H$VZo {ÌH$moU h¢ ?
(A) 23
(B) 27
(C) 29
(D) 31
069. ZrMo {X`o J`o {MÌ ‘| {H$VZo dJ© h¢¡ ?
(A) 20
(B) 13
(C) 24
(D) 17
070. ZrMo {X`o J`o {MÌ ‘| {H$VZo dJ© h¢ ?
(A) 18 (B) 19
(C) 25 (D) 27
4 - DC ] [ 24 ] [ Contd...
071. How many squares are there in the figure below?
(A) 11 (B) 21
(C) 24 (D) 26
072. The figure below is embedded in one of the four alternate figures. Identify it.
(A)
(B)
(C)
(D)
071. ZrMo {X`o J`o {MÌ ‘| {H$VZo dJ© h¢ ?
(A) 11 (B) 21
(C) 24 (D) 26
072. àíZ {MÌ {H$gr EH$ {dH$ën ‘| g‘m{hV h¡& ghr {dH$ën H$mo {MpÝhV H$a|&
(A)
(B)
(C)
(D)
4 - DC ] [ 25 ] [ PTO
073. The figure below is embedded in one of the four alternate figures. Identify it.
(A)
(B)
(C)
(D)
074. Which of the following choices is the exact mirror image of the main figure given. (the mirror is on the right side of the object)
(A) (B)
(C) (D)
073. àíZ {MÌ {H$gr EH$ {dH$ën ‘| g‘m{hV h¡& ghr {dH$ën H$mo {MpÝhV H$a|&
(A)
(B)
(C)
(D)
074. àíZ {MÌ Ho$ ghr Xn©U à{V{~å~ {MÌ H$m M`Z H$a|& (Xn©U dñVw Ho$ Xm{hZo hmW H$s Va’$ h¡)
(A) (B)
(C) (D)
4 - DC ] [ 26 ] [ Contd...
075. Which of the following choices is the exact mirror image of the main figure given. (the mirror is on the right side of the object)
(A)
(B)
(C)
(D)
076. Identify the odd one.
(A) (B) (C) (D)
077. Identify the odd one.
(A) (B) (C) (D)
075. àíZ {MÌ Ho$ ghr Xn©U à{V{~å~ {MÌ H$m M`Z H$a|& (Xn©U dñVw Ho$ Xm{hZo hmW H$s Va’$ h¡)
(A)
(B)
(C)
(D)
076. {dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A) (B) (C) (D)
077. {dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A) (B) (C) (D)
4 - DC ] [ 27 ] [ PTO
078. Identify the odd one.
(A) (B) (C) (D)
079. Identify the odd one.
(A) (B) (C) (D)
080. Hamayun’s Tomb is situated in (A) Punjab (B) Madhya Pradesh (C) Uttar Pradesh (D) Delhi
081. Architect B.V. Doshi Designed (A) IIT Kanpur (B) IIT Delhi (C) IIM Ahmedabad (D) IIM Bengaluru
082. Who designed the city of Chandigarh? (A) Edward Lutyens (B) Richard Rogers (C) Le Corbusier (D) Aldo Rossi
083. Which stone is used in Dilwara temples? (A) Granite (B) Marble (C) Sandstone (D) Kota
078. {dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A) (B) (C) (D)
079. {dH$ënm| ‘| go {^ÝZ dmbo H$mo {MpÝhV H$a|&
(A) (B) (C) (D)
080. hþ‘mD±° H$m ‘H$~am H$hm° h¡ ? (A) n§Om~ (B) ‘Ü` àXoe (C) CËVa àXoe (D) {Xëbr
081. dmñVw{dX ~mb H¥$îU Xmofr Zo BZ g~ ‘| go Š`m {S>OmBZ {H$`m Wm?
(A) AmB©. AmB©. Q>r. H$mZnwa (B) AmB©. AmB©. Q>r. {Xëbr
(C) AmB©. AmB©. E‘. Ah‘Xm~mX (D) AmB©. AmB©. E‘. ~|Jmbwê$
082. MÊS>rJ‹T> {H$gZo {S>OmBZ {H$¶m Wm? (A) ES>dS©> bw{Q>`Ýg (B) [aMS©> am°Og© (C) b H$ma~y{µO¶a (D) EëS>mo amogr
083. {Xbdmam ‘pÝXa H$m¡Z go nËWa go ~Zm h¡? (A) J«oZmBQ> (B) ‘m~©b (C) g¢S>ñQ>moZ (D) H$moQ>m
4 - DC ] [ 28 ] [ Contd...
084. Major component of brick is
(A) Silica (B) Nickel
(C) Carbon (D) Magnesia
085. Which of the following is a flowering tree?
(A) Arjun
(B) Ashok
(C) Teak
(D) Amaltas
086. Which of the following is rock cut temple?
(A) Meenakshi Temple
(B) Kandariya Mahadeo Temple
(C) Kailashanath Temple
(D) Lingraja Temple
087. The three primary colours are
(A) Red, Blue and Yellow
(B) Red, Blue and Green
(C) Red, Blue and Black
(D) Red, White and Black
088. The Extension of the Louvre, Paris, in the form of a pyramid is designed by
(A) Eero Saarinen
(B) I.M.Pei
(C) John Utzon
(D) Jane Drew
084. BªQ> H$s ~ZmdQ> ‘| A{YH$m§e ^mJ {H$gH$m hmoVm h¡?
(A) {g{bH$m (B) {ZŠH$b
(C) H$m~©Z (D) ‘¡J{Z{g`m
085. BZ ‘| go H$m¡Z go no‹S> na a§JrZ ’y$b AmVo h¢?
(A) AO©wZ
(B) AemoH$
(C) Q>rH$
(D) A‘bVmg
086. BZ‘| go H$m¡Z gm "am°H$ H$Q>' ‘pÝXa h¡ ?
(A) ‘rZmjr ‘pÝXa
(B) H$ÝXm[a`m ‘hmXod ‘pÝXa
(C) H¡$bmeZmW ‘pÝXa
(D) qbJamO ‘pÝXa
087. VrZ ‘m¡{bH$ (àmB©‘ar) a§J H$m¡Z go h¢ ?
(A) bmb, Zrbm Am¡a nrbm
(B) bmb, Zrbm Am¡a ham
(C) bmb, Zrbm Am¡a H$mbm
(D) bmb, g’o$X Am¡a H$mbm
088. byd«, n¡[ag' H$m {dñVma (EŠgQ>¡ÝeZ) Omo {H$
EH$ {nam{‘S> H$s Vah h¡, {H$gZo {H$`m Wm ?
(A) E¡amo g¡[aZZ
(B) AmB©. E‘. nmB©.
(C) Om°Z AQ>OZ
(D) OoZ S¯>
4 - DC ] [ 29 ] [ PTO
089. Which of these does not form part of Reinforced Cement Concrete?
(A) Steel
(B) Sand
(C) Lime
(D) Cement
In questions 90-99, identify the logo and select the correct answer from the options below:
090.
(A) IBM
(B) BSNL
(C) TATA
(D) INTEL
091.
(A) Facebook
(B) Firefox
(C) Fiat
(D) Fendi
092.
(A) Make in India
(B) Jaguar
(C) King Power
(D) WWF
089. BZ g~ ‘| go H$m¡Z gm [aBZ’$moñS©> {g‘oÝQ> H$mÝH««$rQ
(R.C.C.) Ho$ g§`moOZ H$m {hñgm Zht hmoVm ?
(A) ñQ>rb
(B) g¢S>
(C) bmB©‘
(D) gr‘oÝQ> àíZ 90-99 ‘| {X`o J`o bmoJmo H$mo nhMmZ| d {X`o JE {dH$ënm| ‘| go ghr CËVa M`Z H$ao|&
090.
(A) AmB©. ~r. E‘.
(B) ~r. Eg. EZ. Eb.
(C) Q>mQ>m
(D) BZQ>¡b
091.
(A) ’o$g~wH$
(B) ’$m`°a’$m°Šg
(C) {’$`Q>
(D) ’o$ÝS>r
092.
(A) ‘oH$ BZ BpÝS>`m
(B) O¡½`ma
(C) qH$J nmda
(D) S>ãë`y. S>ãë`y. E’$.
4 - DC ] [ 30 ] [ Contd...
093.
(A) Adidas
(B) Mahindra
(C) Amazon
(D) Avon
094.
(A) Surya (B) Aadhaar
(C) Phillips (D) ONGC
095.
(A) Mitsubushi (B) Mahendra
(C) Masterchef (D) McDonalds
096.
(A) Chartered Accountant
(B) Council of Auditors
(C) Council of Architecture
(D) Chamber of Auctioneers
097.
(A) Airport Authority of India
(B) Sports Authority of India
(C) Electricity Commission of India
(D) Audit and Accounts Commission
093.
(A) ES>rS>mg
(B) ‘{hÝÐm
(C) A‘oOm°Z
(D) Edm°Z
094.
(A) gy`m© (B) AmYma
(C) {’${bßg (D) Amo. EZ. Or. gr.
095.
(A) {‘Ëgw~wfr (B) ‘{hÝÐm
(C) ‘mñQ>af¡’$ (D) ‘¡H$S>m°ZëS>g
096.
(A) MmQ>©S©> AH$mD$°Q>¢Q>
(B) H$mD$pÝgb Am°’$ Am°{S>Q>g©
(C) H$mD$pÝgb Am°’$ Am{H©$Q>oŠMa
(D) Moå~a Am°’$ H$m°‘g©
097.
(A) E`anmoQ>© AWmo[a{Q> Am°’$ BpÝS>`m
(B) ñnmoQ>²©g AWmo[a{Q> Am°’$ BpÝS>`m
(C) Bb¡pŠQ´{gQ>r H${‘eZ Am°’$ BpÝS>`m
(D) Am°{S>Q> EÊS> AH$mD$§Q²g H${‘eZ
4 - DC ] [ 31 ] [ PTO
098.
(A) Asian Paints
(B) Digital India
(C) Planning Commission
(D) Smart City
099.
(A) State Bank of India
(B) Metro
(C) Uber
(D) Oriental Bank of Commerce
100. Select the correct figure from the options to continue the series to replace the question mark.
(A) (B)
(C) (D)
098.
(A) E{e`Z noÝQ²g
(B) {S>OrQ>b BpÝS>`m
(C) ßb¡qZJ H${‘eZ
(D) ñ‘mQ>© {g{Q>
099.
(A) ñQ>oQ> ~¢H$ Am°’$ BpÝS>`m
(B) ‘¡Q´mo
(C) D$~oa
(D) Amo[aE§Q>b ~¢H$ Am°’$ H$m°‘g©
100. {dH$ënm| ‘| go {H$gr EH$ H$m M`Z H$a| Omo àíZ {MÌ H$s loUr nyar H$aoJm&
(A) (B)
(C) (D)
4 - DC ] [ 32 ]
SPACE FOR ROUGH WORK / H$ÀMo H$m‘ Ho$ {b¶o OJh
